Q: What happens if the Cultist wins by causing the Dunwich Horror, but someone else then plays the Secret Cultist? Which one of them wins?

A: We would say that the Secret Cultist’s win trumps that of the overt Cultist.  Surprises are meant to Surprise the other players, and prevent what would have normally happened, and make something else happen.  So, in this case, the Cultist is expecting to win, but… Surprise!  The Secret Cultist has been machinating behind his back…